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Erlang C calculator — free contact center staffing tool

Enter your call volume, average handle time, and service level target. The calculator applies the Erlang C formula to output the minimum agents needed, agent utilization, expected wait time, and a full service-level table so you can see the cost of staffing above or below target.

Calculator inputs

Inbound volume in your planning interval — use peak hour

Talk time + after-call work (ACW) combined

The "T" in your service level — 20s for the standard 80/20

The "X%" in your target — 80 for 80/20, 90 for 90/20

What is the Erlang C formula?

The Erlang C formula calculates the probability that an incoming call must wait in queue before an agent becomes available. Developed by Agner Krarup Erlang in 1917 for telephone network engineering, it remains the mathematical foundation underneath every contact center WFM system.

The core output is PC — the probability of waiting. Two further numbers follow:

  • Expected wait time for callers who do queue = PC × AHT ÷ (N − A), where N is agent count and A is traffic intensity in Erlangs
  • Service level = 1 − PC × e−(N − A) × T ÷ AHT, where T is target answer time

Traffic intensity in Erlangs = (calls per hour × AHT in minutes) ÷ 60. At 120 calls/hr with 5-min AHT: A = 10 Erlangs. You always need N > A — at exactly N = A, every agent runs at 100% occupancy, queues never clear, and any service level target is impossible.

The 80/20 service level standard

80/20 means 80% of calls answered within 20 seconds. It became the industry default through Bell System network design and ICMI research in the 1980s. Most ACD platforms, COPC certifications, and outsourcer SLAs use it as the baseline measurement.

80/20 is not a universal law. Healthcare triage queues target 80/30 or 90/20. High-net-worth financial lines run 90/10. Emergency dispatch targets 95/5. E-commerce during peak season may negotiate 70/30 as a cost trade-off. The right target is the answer time your callers will tolerate before abandoning — which you measure from your own ACD abandon curve.

Industry / queue type Typical target Reason
General contact center80/20ICMI / COPC default
Healthcare triage80/30 or 90/20Patient urgency
Financial services HNW90/10 or 95/15Client retention risk
Emergency dispatch95/5 or 99/5Public safety mandate
E-commerce peak season70/30 – 80/30Cost vs. volume trade-off

From Erlang C output to a weekly staffing plan

  1. Export your ACD report: calls received and AHT per 30-minute interval for the busiest week.
  2. Run the calculator for each interval using the actual volume and AHT for that slot.
  3. Add 15–20% shrinkage to each interval's agent count — covers paid breaks, team meetings, training, coaching, and unplanned absences.
  4. Group intervals into feasible shift patterns (8h, 10h). Use the per-interval gross FTE demand as a scheduling constraint.
  5. Rerun monthly. Call volume and AHT shift seasonally; staffing models built on data older than 6 months are usually wrong.

WFM platforms — Verint, Calabrio, NICE WFM, and DialPhone's built-in WFM module — automate all five steps. The Erlang C formula is the engine underneath them. It is worth understanding whether or not you use a dedicated WFM system.

Assumptions and limitations

Erlang C is accurate when these conditions hold:

  • Poisson arrivals — calls arrive randomly and independently. Holds well for most inbound queues.
  • Exponential service times — handle times vary around the mean exponentially. Reasonable approximation for most call types.
  • Infinite patience — no abandonment. This is the formula's main limitation. Real callers hang up, reducing queue pressure. Erlang C slightly overstates required agents as a result. For abandon rates consistently above 10%, use Erlang A or simulation.
  • Homogeneous agents — all agents handle calls at the same average rate. Skills-based routing and specialist queues reduce effective capacity below the formula's prediction.

For most planning scenarios with under 5% abandonment and broad-skill agents, Erlang C is sufficiently accurate. Add 10–15% headroom where in doubt.

FAQ: Erlang C and contact center staffing

What is the Erlang C formula?
Erlang C calculates the probability that an incoming call will have to wait in queue before being answered. Developed by Danish mathematician Agner Krarup Erlang in 1917 for telephone traffic engineering, it is the mathematical foundation of every contact center workforce management system. The three inputs are offered traffic in Erlangs, number of agents, and target answer time. The outputs are: probability of waiting, expected wait for callers who do queue, and service level — the percentage of calls answered within the target time.
What is traffic intensity measured in Erlangs?
Traffic intensity in Erlangs = (calls per hour × average handle time in minutes) ÷ 60. Example: 120 calls per hour with 5-minute AHT = 10 Erlangs. Erlangs represent the average number of calls in progress simultaneously. You always need more agents than Erlangs — at exactly N agents and N Erlangs every agent is permanently busy, queues grow to infinity, and no service level target is achievable.
What is the 80/20 service level standard?
80/20 means 80% of calls answered within 20 seconds. It became the contact center default through Bell System network design and ICMI research. Most ACD platforms, COPC certification frameworks, and outsourcer SLAs use 80/20 as baseline. Healthcare often targets 80/30 or 90/20. Financial services high-net-worth lines target 90/10. Emergency dispatch runs 95/5. The right target depends on your callers, not the industry default.
What are the limitations of Erlang C?
Erlang C assumes: Poisson-distributed arrivals, exponential service times, infinite caller patience (no abandonment), and identical agents. The infinite patience assumption is the critical limitation. Real callers hang up, which reduces queue pressure. Erlang C therefore slightly overstates required agents. For operations with abandon rates consistently above 10%, use Erlang A (the abandonment-aware variant) or simulation. For rough planning under 5% abandonment, Erlang C is accurate enough.
How do I convert Erlang C output into a weekly FTE budget?
Add 15-20% shrinkage to the Erlang C agent count. Shrinkage covers paid breaks, training sessions, coaching, and unplanned absences. A contact center needing 12 agents per Erlang C during peak needs 14-15 scheduled FTEs to maintain that service level with realistic occupancy. Run the calculator for each 30-minute interval across your busiest week, apply shrinkage per interval, then build shift patterns that cover demand.
Does Erlang C work for chat and email queues?
Erlang C was designed for voice queues where one agent handles one contact at a time. For chat where agents handle two to three simultaneous conversations, a modified formula or simulation is more accurate. For email queues with flexible SLAs, simple throughput models are sufficient. Voice remains the primary use case. For omnichannel operations, run separate Erlang C calculations per channel and sum the FTE requirements.

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